Commun. Comput. Phys., 8 (2010), pp. 1264-1271.

A Hybrid Numerical Method to Cure Numerical Shock Instability

Hao Wu 1*, Longjun Shen 1, Zhijun Shen 1

1 Institute of Applied Physics and Computational Mathematics, Beijing, P.O. Box 8009, 100088, China.

Received 4 October 2009; Accepted (in revised version) 27 April 2010
Available online 28 July 2010


In this note, we propose a new method to cure numerical shock instability by hybriding different numerical fluxes in the two-dimensional Euler equations. The idea of this method is to combine a "full-wave" Riemann solver and a "less-wave" Riemann solver, which uses a special modified weight based on the difference in velocity vectors. It is also found that such blending does not need to be implemented in all equations of the Euler system. We point out that the proposed method is easily extended to other "full-wave" fluxes that suffer from shock instability. Some benchmark problems are presented to validate the proposed method.

AMS subject classifications: 52B10, 65D18, 68U05, 68U07

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Key words: Godunov methods, numerical shock instability, carbuncle phenomenon.

*Corresponding author.
Email: (H. Wu), (L. Shen), (Z. Shen)

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